I do not understand substitution

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Like described in image, I do not know how P1 become like that. Especially about why p1 is removed. Is there any formula used for this question?

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The equation is of the form

$$P_1=a+bP_1$$ which you rewrite

$$(1-b)P_1=a,$$ $$P_1=\frac a{1-b}.$$